Starting with conceptual understanding is key to building procedural fluency in math
The foundation of a strong mathematical education lies in conceptual understanding rather than rushing to teach algorithms. As educators, the speakers emphasize the importance of starting with conceptual learning to build procedural fluency. This approach not only helps children grasp the ‘why’ behind the math but also sets them up for success in more advanced topics like algebra. By focusing on the conceptual aspects, you can help your child develop a robust understanding that will serve them well throughout their educational journey.
Understanding Math: The Importance of Conceptual Learning Over Algorithms
Last updated:
As a parent of a child struggling with math, you might feel overwhelmed by the complexities of the subject and the pressure to ensure your child’s success. The journey through math education can be daunting, especially when traditional teaching methods focus heavily on algorithms rather than conceptual understanding. However, it’s crucial to recognize that schools may not always provide the support your child needs, but you can make a significant difference by leveraging available tools and resources to foster a deeper understanding of math concepts.
Multi-digit multiplication as a gateway to advanced math concepts
One specific example highlighted is multi-digit multiplication. When taught conceptually from the start, it can stretch into algebra and even complex high school topics like completing the square. By using tools like arrays and open arrays, you can guide your child to draw connections between elementary math and higher-level concepts. This method not only makes math more accessible but also more engaging for your child, helping them see the relevance and beauty of the subject.
Author Quote
"
It’s more about gradually pushing along this trajectory… We shouldn’t be abandoning the original conceptual piece. We should be coming back every so often so that we don’t lose sight.
"
The dangers of rushing to algorithms and the importance of understanding the ‘why’
Rushing to algorithms can undermine a child’s ability to think deeply about math. The speakers caution against replacing one algorithm with another without understanding the underlying concepts. For instance, using the ‘box method’ without connecting it to arrays and area models can lead to memorization rather than understanding. As a parent, it’s your responsibility to encourage your child to explore the ‘why’ behind the math, ensuring they don’t just follow steps but truly comprehend the material.
Key Takeaways:
1
Build Conceptual Understanding First: It's crucial for parents to encourage their children to develop a deep conceptual understanding of mathematical concepts before focusing on procedural fluency. For instance, using arrays and open arrays to teach multi-digit multiplication can help children understand the underlying principles, which can later be connected to more complex topics like algebra and quadratic equations. This approach helps in building a strong foundation that supports long-term learning and problem-solving skills.
2
Avoid Rushing to Algorithms: Parents should be cautious about relying solely on algorithms or procedural methods, as this can hinder a child's ability to understand the 'why' behind the math. For example, instead of teaching children to use the box method or cross multiplication as quick fixes, encourage them to explore the conceptual reasons behind these methods, such as understanding area models or proportional relationships. This helps prevent the replacement of one algorithm with another without true understanding.
3
Introduce Key Concepts Early and Contextually: Parents can help their children by introducing fundamental concepts like fractions, decimals, and percentages as operators early in their education, using real-life contexts. Encouraging children to estimate and reason about quantities, such as understanding what a quarter of a group or 28% of a number means, can make these concepts less intimidating and more relatable. This early exposure can lay the groundwork for understanding proportional relationships and enhance their mathematical reasoning skills as they progress through school.
Introducing fractions, decimals, and percents as operators early can enhance spatial reasoning and core math skills
Another critical area is the introduction of fractions, decimals, and percents as operators. These concepts are often introduced too late and taught procedurally, which can be detrimental to a child’s understanding. By introducing benchmark fractions early and encouraging estimation and spatial reasoning, you can help your child develop a strong foundation in these areas. Utilizing tools like Core Skills of Math and focusing on Spatial Reasoning can enhance your child’s ability to understand the relative size of quantities and make math less intimidating.
Author Quote
"
These are moves that if we’re intentional enough about them, we can make such a significant difference in how students approach this what what is often a very very foggy and scary sort of content area for students, fractions, decimals, percents.
"Overcoming the challenge of proportional relationships for a better math education
One specific challenge mentioned is the difficulty students face with proportional relationships, often due to an over-reliance on algorithms like cross multiplication. As a parent, your role is crucial in helping your child overcome this challenge. By using tools like double number lines and focusing on conceptual understanding, you can guide your child to solve proportional problems with ease. Utilizing resources like Core Skills of Math and Spatial Reasoning can empower your child to think critically and confidently, leading to a more positive and successful math education.
Empower your child’s math journey with conceptual understanding using the Brain Bloom System, designed to help them overcome learning challenges and thrive in math.
